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Description: |
The multivariate data fitting problem occurs frequently in many branches of science and engineering. It is very easy to fit a data set exactly by a mathematical model no matter how the data points are distributed. But building a response by using a limited number of poorly distributed data points is very unreliable, yet necessary in conceptual design process. This study documents the lessons learned from fitting the wing weight data of 41 subsonic transports by three types of interpolation methods -- least polynomial interpolation, radial basis function interpolation, and Kriging interpolation. The objective of this study is to develop an automatic procedure of using these interpolation methods for construction of an approximation of the relationship between the actual wing weight and various key configuration parameters of wing by using actual wing weight data of 41 subsonic transports. The focus of the study is on four key technical issues in practical use of approximation methods: data generation and variable screening, fitting the data by a parametric function model, tuning intrinsic model parameters by using cross-validation, and verification of constructed approximation. One controversial topic is the assessment of the constructed approximations, which is of great importance to practitioners but depends too much on subjective judgment. Some formal approaches for the assessment will be proposed and analyzed. Even though the benefits of using principal component regression with cross validation are only demonstrated by the wing weight data fitting problem, the proposed methodology could have significant advantages in fitting other historical or hard-to-obtain data.
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